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Quantum information theory has shown strong connections with classical statistical physics. For example, quantum error correcting codes like the surface and the color code present a tolerance to qubit loss that is related to the classical…
Mixed-state phases of matter under local decoherence have recently garnered significant attention due to the ubiquitous presence of noise in current quantum processors. One of the key issues is understanding how topological quantum memory…
Quantum error correction plays a critical role in enabling fault-tolerant quantum computing by protecting fragile quantum information from noise. While general-purpose quantum error correction codes are designed to address a wide range of…
A promising approach to overcome decoherence in quantum computing schemes is to perform active quantum error correction using topology. Topological subsystem codes incorporate both the benefits of topological and subsystem codes, allowing…
We construct two-dimensional codes for correcting burst errors using the finite field Fourier transform. The encoding procedure is performed in the transformed domain using the conjugacy property of the finite field Fourier transform. The…
The main ideas of quantum error correction are introduced. These are encoding, extraction of syndromes, error operators, and code construction. It is shown that general noise and relaxation of a set of 2-state quantum systems can always be…
Quantum error correcting codes (QECCs) are the means of choice whenever quantum systems suffer errors, e.g., due to imperfect devices, environments, or faulty channels. By now, a plethora of families of codes is known, but there is no…
Quantum networks aim to facilitate the fault-tolerant and secure transmission of quantum states across distant devices. The widely adopted quantum teleportation scheme requires multiple rounds of entanglement swapping and purification,…
Homological quantum error correction uses tools of algebraic topology and homological algebra to derive Calderbank-Shor-Steane quantum error correcting codes from cellulations of topological spaces. This work is an exploration of the…
Quantum computation and communication rely on the ability to manipulate quantum states robustly and with high fidelity. Thus, some form of error correction is needed to protect fragile quantum superposition states from corruption by…
Quantum error correction is a crucial tool for mitigating hardware errors in quantum computers by encoding logical information into multiple physical qubits. However, no single error-correcting code allows for an intrinsically…
We study the error threshold of color codes, a class of topological quantum codes that allow a direct implementation of quantum Clifford gates suitable for entanglement distillation, teleportation and fault-tolerant quantum computation. We…
A big open question in the quantum information theory concerns feasibility of a self-correcting quantum memory. A quantum state recorded in such memory can be stored reliably for a macroscopic time without need for active error correction…
Typically, fault-tolerant operations and code concatenation are reserved for quantum error correction due to their resource overhead. Here, we show that fault tolerant operations have a large impact on the performance of symmetry based…
Quantum error correction (QEC) codes can tolerate hardware errors by encoding fault-tolerant logical qubits using redundant physical qubits and detecting errors using parity checks. Leakage errors occur in quantum systems when a qubit…
Quantum computers herald the arrival of a new era in which previously intractable computational problems will be solved efficiently. However, quantum technology is held down by decoherence, a phenomenon that is omnipresent in the quantum…
We prove the existence of topological quantum error correcting codes with encoding rates $k/n$ asymptotically approaching the maximum possible value. Explicit constructions of these topological codes are presented using surfaces of…
Quantum error correction protects fragile quantum information by encoding it into a larger quantum system. These extra degrees of freedom enable the detection and correction of errors, but also increase the operational complexity of the…
Modern lattice-based cryptography, particularly the learning with errors paradigm, relies on injecting artificial noise to secure data against quantum adversaries. This study systematically examines the theoretical and physical boundaries…
Large-scale quantum computers will inevitably need quantum error correction (QEC) to protect information against decoherence. Given that the overhead of such error correction is often formidable, autonomous quantum error correction (AQEC)…